Authors´ Reply to “Comments on Unique Extraction of Metamaterial Parameters Based on Kramers–Kronig Relationship”

In replying, the authors of the original work [ibid., vol. 58, no. 10, pp. 2646-2653, Oct. 2010] would like to address the comments by J.J. Barroso and U. C. Hasar ["Comments on \´A unique extraction of metamaterial parameters based on Kramers-Kronig relationship\´" - see ibid., vol. 60, no. 6, pp. 1743-1744, Jun. 2012]. Their main objection is that the commentors do not take into consideration that real metamaterials has finite unit cell size, and especially, the experimentally reported double-negative metamaterials has unit cells, which are not deep subwavelength. In case of metamaterials constructed from small resonators, the strength of the resonance decreases with the decrease in the unit cell size; hence, for deep sub-wavelength elements, the strength of the resonance is not strong enough to produce negative magnetic permeability. The double-negative metamaterials can support higher order modes at frequencies that are just slightly different than the frequency region where the double-negative behavior occurs. Therefore, special care must be taken when effective material parameters are extracted, and it is not sufficient to enforce the continuity of the refractive index obtained from transmission reflection measurements or calculations because we can extract erroneous effective material parameters for frequency regions where they do not even exist.